Question: Simplify the following expression: $ r = \dfrac{-10}{9} - \dfrac{-2z}{z - 10} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{z - 10}{z - 10}$ $ \dfrac{-10}{9} \times \dfrac{z - 10}{z - 10} = \dfrac{-10z + 100}{9z - 90} $ Multiply the second expression by $\dfrac{9}{9}$ $ \dfrac{-2z}{z - 10} \times \dfrac{9}{9} = \dfrac{-18z}{9z - 90} $ Therefore $ r = \dfrac{-10z + 100}{9z - 90} - \dfrac{-18z}{9z - 90} $ Now the expressions have the same denominator we can simply subtract the numerators: $r = \dfrac{-10z + 100 + 18z }{9z - 90} $ Distribute the negative sign: $r = \dfrac{-10z + 100 + 18z}{9z - 90}$ $r = \dfrac{8z + 100}{9z - 90}$